1,011 research outputs found
Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
Recent work suggests that a sharp definition of `phase of matter' can be
given for some quantum systems out of equilibrium---first for many-body
localized systems with time independent Hamiltonians and more recently for
periodically driven or Floquet localized systems. In this work we propose a
classification of the finite abelian symmetry protected phases of interacting
Floquet localized systems in one dimension. We find that the different Floquet
phases correspond to elements of , where
is the undriven interacting classification, and is
a set of (twisted) 1d representations of . We will address symmetry broken
phases in a subsequent paper.Comment: 21 pages. Explained connection to the classification schemes in other
recent work. Close to published versio
1D Many-body localized Floquet systems II: Symmetry-Broken phases
Recent work suggests that a sharp definition of `phase of matter' can be
given for periodically driven `Floquet' quantum systems exhibiting many-body
localization. In this work we propose a classification of the phases of
interacting Floquet localized systems with (completely) spontaneously broken
symmetries -- we focus on the one dimensional case, but our results appear to
generalize to higher dimensions. We find that the different Floquet phases
correspond to elements of , the centre of the symmetry group in question.
In a previous paper we offered a companion classification of unbroken, i.e.,
paramagnetic phases.Comment: Published versio
Richard Charles Murphy — Guestworkers in the German Reich: A Polish Community in Wilhelmian Germany.
Sub-ballistic growth of R\'enyi entropies due to diffusion
We investigate the dynamics of quantum entanglement after a global quench and
uncover a qualitative difference between the behavior of the von Neumann
entropy and higher R\'enyi entropies. We argue that the latter generically grow
\emph{sub-ballistically}, as , in systems with diffusive
transport. We provide strong evidence for this in both a U symmetric
random circuit model and in a paradigmatic non-integrable spin chain, where
energy is the sole conserved quantity. We interpret our results as a
consequence of local quantum fluctuations in conserved densities, whose
behavior is controlled by diffusion, and use the random circuit model to derive
an effective description. We also discuss the late-time behavior of the second
R\'enyi entropy and show that it exhibits hydrodynamic tails with \emph{three
distinct power laws} occurring for different classes of initial states.Comment: close to published version: 4 + epsilon pages, 3 figures + supplemen
Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
The scrambling of quantum information in closed many-body systems, as
measured by out-of-time-ordered correlation functions (OTOCs), has lately
received considerable attention. Recently, a hydrodynamical description of
OTOCs has emerged from considering random local circuits, aspects of which are
conjectured to be universal to ergodic many-body systems, even without
randomness. Here we extend this approach to systems with locally conserved
quantities (e.g., energy). We do this by considering local random unitary
circuits with a conserved U charge and argue, with numerical and
analytical evidence, that the presence of a conservation law slows relaxation
in both time ordered {\textit{and}} out-of-time-ordered correlation functions,
both can have a diffusively relaxing component or "hydrodynamic tail" at late
times. We verify the presence of such tails also in a deterministic,
peridocially driven system. We show that for OTOCs, the combination of
diffusive and ballistic components leads to a wave front with a specific,
asymmetric shape, decaying as a power law behind the front. These results also
explain existing numerical investigations in non-noisy ergodic systems with
energy conservation. Moreover, we consider OTOCs in Gibbs states, parametrized
by a chemical potential , and apply perturbative arguments to show that
for the ballistic front of information-spreading can only develop at
times exponentially large in -- with the information traveling
diffusively at earlier times. We also develop a new formalism for describing
OTOCs and operator spreading, which allows us to interpret the saturation of
OTOCs as a form of thermalization on the Hilbert space of operators.Comment: Close to published version: 17 + 9.5 pages. Improved presentation.
Contains new section on clean Floquet spin chain. New and/or improved
numerical data in Figures 4-7, 11, 1
STEVEN E. OZMENT. — The Reformation in the Cities. The Appeal of Protestantism to Sixteenth-Century Germany and Switzerland.
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